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Questions tagged [kerr-metric]

The Kerr metric describes the geometry of empty spacetime around a rotating uncharged axially-symmetric black hole.

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How to derive Smarr formula for Kerr Black Hole?

Following is the Smarr formula for Kerr Black Hole $$M=\frac{\kappa A}{4\pi}+2 \Omega J $$ where $\kappa, \Omega$, $J$ and $A$ are surface gravity, angular velocity, angular momentum and surface area ...
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Quantum field expansion and bogoliubov coefficients in the interior of a rotating black hole

I am trying to quantize a real scalar field in the interior of a rotating black hole (3+1 D, asymptotically flat). My question is regarding the modes of the radial part of the equation (obtained after ...
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How does loop quantum gravity handle spacetimes which aren't globally hyperbolic, like the Kerr metric?

Loop quantum gravity assumes spacetime is globally hyperbolic. However, the interior of a Kerr black hole isn't globally hyperbolic, containing closed timelike curves. So, how are Kerr black holes ...
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Checking inverse metric and Christoffel symbols for the Kerr metric against references

I am trying to cross-check the Christoffel symbols and other very laborious geometric components in several metrics. In particular the Kerr metric is notoriously complex and results in expressions ...
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Can a Kerr black hole become super-extremal?

Let's assume there is a large Kerr black hole, which is almost extremal and would become extremal with the addition of a small amount of mass $M$ with spin $J$ to make the final $J=M$. What if this ...
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What happens to the ring singularities when two Kerr black holes merge?

Imagine two Kerr black holes with ring singularities oriented in different axes (e.g. one horizontal and the other one vertical). If they merge, what will happen to these singularities? Will they form ...
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What are spinning black holes orbiting?

I have seen depictions of spinning black holes with the "singularity" spinning around a center of rotation in a flat plane, or moving around an imaginary sphere. Is there anything in the ...
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Is the Schwarzschild singularity a limit of the Kerr singularity?

In a Schwarzschild black hole, the singularity is spacelike. In a Kerr black hole, it is timelike. Is there any continuous transformation between those solutions? Can the Schwarzschild solution be ...
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Can ring singularities form a Hopf link?

Can ring singularities form a Hopf link?
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Why domain of Kerr black hole includes negative values for $r$ coordinate?

I understand the domain of $t$ is all real numbers but mathematically, how to prove the domain of $r$ coordinate is also all real numbers except $r=0$ when $\theta = \pi/2$. I know that we get two ...
Talha Ahmed's user avatar
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Does someone falling into a spinning black hole see the end of the universe?

It is well known that if you fall into the Schwarzschild black hole you cannot see the entirety of the outside spacetime since there are photons which cannot catch up with you before you reach the ...
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Angular velocity of stationary observer

I am studying Kerr metric in Boyer Lindquist coordinates and having trouble in understanding the components of angular velocity of stationary observer with constant r and $\theta$ motion w.r.t ...
Talha Ahmed's user avatar
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Significance of simultaneous transformation of $t$ and $\phi$ in kerr metric

The Kerr metric in Boyer-Lindquist coordinate is invariant under simultaneous transformations $t \rightarrow -t$ and $\phi \rightarrow -\phi$ but not invariant if we apply one transformation only. ...
Talha Ahmed's user avatar
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Perimeter of Kerr's event horizon

We can compute the "proper circumference" of the Schwarzschild event horizon integrating its line element along its perimeter at a fixed $t$. This would be the minimum length of a rope that ...
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Is it possible to refind entry trajectory after leaving a rotating black hole?

I'm asking about the case where an infalling object travels a path right through a rotating black hole, intact. I want to provide a simple parallel for the purposes of question clarity: A horse can ...
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What actually is Boyer-Lindquist coordinates?

I want to know the difference between spherical and Boyer-Lindquist coordinates. Don't they both use $r, \theta, \phi$ parameters? I've searched books and sources on the internet and there's none that ...
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Gray body factors of PBH's - radial equation approximation (Page 1976)

I'm deriving the results of the Page paper: "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole*" (https://doi.org/10.1103/PhysRevD.13.198). At ...
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What happens if $ a^2 > M^2 $ in Kerr metric?

(Boyer-Lindquist coordinates and $ c = G =1 $ taken) As I know, line element in Kerr metric $ d s^2 = - \left( 1 - \frac{2Mr}{\rho^2} \right) d t^2 - \frac{4 M a r \sin^2 \theta}{\rho^2} d \phi d t + \...
posfn0319's user avatar
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Is it possible that black holes spin in discreet spin quanta?

Roy Kerr recently wrote a paper critical of the Penrose singularity theorem. One interpretation of his paper is that the singularity problem might be an artifact of the Schwarzchild metric and that a ...
Daniel Shulman's user avatar
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The Kerr metric applied to a solid rotating body

Can the Kerr metric be used as an exterior solution to analyse the vacuum outside a rotating solid body or does it only apply to a rotating black hole? If it can't, is there an alternative exterior ...
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Calculating the determinant of the Kerr metric

I have been trying to calculate the determinant of the Kerr metric (described by equation 11.71, A First Course in General Relativity: 3rd Edition, B. Schutz): $$\begin{align}ds^2 &=-\frac{(\Delta-...
Potato salad's user avatar
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Finding the Four-Velocity vector in the Kerr spacetime between two points?

For over a year me and a friend have been working on a Kerr Black Hole renderer. We are close to the finish line and get renders like these; These renders show aberration of light due to the cameras ...
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Causality violation in Kerr metric

my professor told me that in Kerr metric, there is a zone of causality violation around the ring singularity, but he was saying this in the context of $M^2>a^2$, does this also apply to the cases ...
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Question on the transformation from Boyer-Lindquist to Kerr-Schild coordinates, for a modified Kerr metric

From Kerr metric, we do know that there exist a function with the form of: $$\Delta = r^2 - 2 M r + a^2 \tag{1}.$$ Following $[1]$, I did understand the coordinate transformation from Boyer-Lindquist (...
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Hawking radiation from photons?

I am reading a lot of papers that derive the Hawking temperature solving either the Klein Gordon equation for scalar fields or the Dirac equation for spin $\tfrac12$ particles via tunnelling ...
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Question about Kerr's recent paper regarding Penrose et al.'s works on gravitational singularities [duplicate]

R. Kerr posted an essay on arxiv recently. Kerr claims: The consensus view for sixty years has been that all black holes have singularities. There is no direct proof of this, only the papers by ...
Daddy Kropotkin's user avatar
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Is it possible for an object on an initially retrograde orbit to pass through the ergosphere or a rotating black hole and emerge?

I say "initially retrograde" because am aware that while inside the ergosphere, everything necessarily has prograde motion. So the two options I can envision are: The object approaches the ...
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What metric can describe best the spacetime outside a rotating star?

I hope this question is not mistreated as a duplicate, because that is not my intention. The Kerr metric suffices to describe the exterior solution to an axisymmetric spacetime mass distribution of ...
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Asymptotic development of the black-hole metric

In the Kruskal-Szekeres extension of the Schwarzschild metric parallel universes appear. In a couple of questions on this site, for instance: Where does the parallel universe in the Penrose diagram ...
Frederic Thomas's user avatar
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Why does Roy Kerr claim that the Kerr black hole does not contain a singularity?

In a preprint posted on the arXiv, Roy Kerr claims that there is a widespread misunderstanding related to the singularity inside the black hole that bears his name. Can anyone explain his argument in ...
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Redshift near Kerr Black Hole

The question is related to Sean Carroll's Spacetime and Geometry ex 6.6. Consider a Kerr black hole with an accretion disk of negligible mass. Particles in the disk follow geodesics. Some iron in the ...
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Schwarzschild and Kerr solution in $(x, y, z, t)$ coordinates?

The Schwarzschild solution ('simple' black holes) and the Kerr solution (rotating black holes) are very well known in General Relativity. The coordinates which are used to describe them are mostly ...
MartyMcFly's user avatar
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Rotating Black Holes and Birkhoff's theorem

I found a few questions that are similar to mine, but I do not think that either of them answers exactly what I want: Is there a Birkhoff-like theorem for stationary axisymmetric metrics? or ...
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Coordinate transform of Kerr metric to Kerr-Schild coordinates

the transformation from Boyer-Lindquist $\{t,r,\theta,\phi\}$ coordinates to Kerr-Schild $\{t',r,\theta,\phi' \}$coordinates can be written as $$ dt' = dt + \frac{2 M r}{r^2 - 2 M r + a^2} dr, \;\;\; ...
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How to describe the four-current of a tilted loop in Kerr spacetime

consider the Kerr metric in Boyer-Lindquist coordinates. We usually describe the source of an electromagnetic field by the four vector $J^\mu$. $$J^\mu = \{\rho, j^1, j^2, j^3\}.$$ Now we have an ...
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Is there a distance at which the Kerr metric looks like the Schwarzschild metric?

As the title says: Is there a distance at which the Kerr metric looks like Schwarzschild metric? Edit: if there isn't any such distance (smaller than infinity), can we measure from the outside, with ...
MartyMcFly's user avatar
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Spheroidal eigenvalues with shifted boundary conditions

I was studying the spheroidal differential equation in relation to calculating solutions for fields in a general Kerr background metric and, as far as I can tell, the eigenvalues $\lambda$ that enter ...
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What vacuum should be defined for a observer in Kerr spacetime?

A scalar field in Kerr spacetime can have two kinds of modes, one labeled by "in", and the other by "up". The "in" modes originate from the past null infinity, while the &...
Haorong Wu's user avatar
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Carter Constant with a Cosmological Constant

The Carter constant for the Kerr Newman metric $$ \rm C = p_{\theta}^{2} + \cos^{2}\theta \ \Bigg[ a^2 \ (m^2 - E^2) + \left(\frac{L_z}{\sin\theta} \right)^{2} \Bigg] $$ with (in $[+---]$ signature) $$...
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What are the effects on a stationary observer at a specific distance from a Kerr Black Hole?

A Kerr Black Hole (BH) is a spinning BH. There is an Event Horizon (EH) which is $$r_H^\pm =\frac{r_{S} \pm \sqrt{r_{S}^2 - 4a^2}}{2},$$ where $a = \frac{J}{Mc}$ and $r_{S}$ is the Schwarzschild ...
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Physical meaning of Boyer-Lindquist coordinate

The Kerr metric in the Boyer-Linquist coordinate is $$\mathrm{d} s^{2}= \frac{\Delta}{R^{2}}\left(\mathrm{d} t-a \sin ^{2} \theta\, \mathrm{d} \phi\right)^{2}-\frac{\sin ^{2} \theta}{R^{2}}\left[\...
David Shaw's user avatar
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Spacetime metrics extended to negative radius

In the Kerr metric $$ ds^2=\left(1-\frac{2Mr}{\rho^2}\right)dt^2+\frac{4Mar\sin^2\theta}{\rho^2}dtd\varphi-\frac{\rho^2}{\Delta}dr^2-\rho^2d\theta^2-\left(r^2+a^2+\frac{2Ma^2r\sin^2\theta}{\rho^2}\...
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What would Hawking radiation look like from inside the event horizon?

Let’s say you fell into a rotating black hole, the inner horizon of the black hole is an infinite blue shift surface, so you should be able to observe events from the arbitrarily far future before ...
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Why are there two interior regions in this diagram?

Why are there two interior regions in this diagram? There seems to be two inner horizons, and two wormhole regions. Where do the two such regions comes from? What determines which reason someone falls ...
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Where do the other black holes in this diagram come from?

In this Penrose diagram for a charged/Rotating black hole, once your in the new universe you can continue onward to an infinite sequence of black holes/white holes. So I'm asking, where do those black ...
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Blandford-Znajek process - energy flow reverse and other questions

In the original BZ paper [1] from 1977, the authors invoke a number of facts and conclusions that I do not quite follow. In the hope that someone has read it and was able to grasp all the details, I ...
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What happens when two ergospheres of oppositely spinning black holes of the same mass, axis of rotation, and angular momentum approach?

What happens when two ergospheres of oppositely spinning black holes of the same mass, axis of rotation, and angular momentum approach each other? What would happen to the black holes in question?
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How can I make the Kerr black hole surfaces scale well in my diagrams?

I've read that the equatorial radius of the ergosphere of a rotating black hole is the Schwarzschild radius. But in this animation made in natural units by Yukterez it doesn't apply. I then used ...
Stellar_Enginner's user avatar
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Could a Star orbit a rotating black hole inside the ergosphere? If so, how big should the black hole be? [duplicate]

Could a Star orbit a rotating black hole inside the ergosphere? If so, how big should the black hole be? I imagine it should be absolutely massive so that tidal forces are minimal. And if all this is ...
Stellar_Enginner's user avatar
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A question about Kerr black holes and Hawking radiation

It's a common myth that somoene falling into a black hole will see the entire history of the universe before they cross the event horizon. With a Kerr black hole however, it's sort of true. The inner ...
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